WO2006026890A1

WO2006026890A1 - Method for calculating a downlink beamforming weight vector in a wireless communication system

Info

Publication number: WO2006026890A1
Application number: PCT/CN2004/001022
Authority: WO
Inventors: Mattias WENNSTRÖM
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2004-09-06
Filing date: 2004-09-06
Publication date: 2006-03-16

Abstract

The present invention discloses a method for calculating a downlink bearnforming weight vector in a wireless communication system where a pilot channel and a traffic channel beamforming weight vectors are independently chosen, comprising, a) estimating an uplink channel to obtain its coefficient matrix; b) calculating a gram matrix of the uplink channel coefficient matrix; c) filtering the gram matrix; d) finding the downlink beamforming weight vector by maximizing a product of the downlink beamforming weight Herinitian transpose and the filtered gram matrix and the pilot weight vector. The method finds the optimal weight vector for the downlink transmission directly using an analytical expression. In this way, the bit error rate is lower than that of the prior art.

Description

METHOD FOR CALCULATING A DOWNLINK

BEAMFORMING WEIGHT VECTOR IN A WIRELESS

COMMUNICATION SYSTEM

Field of the Technology

The present invention relates to downlink beamforming technology in frequency division duplex radio cellular mobile communications where downlink beamforming is used, more especially to a method for calculating a downlink beamforming weight vector.

Background of the Invention

Antenna arrays are used in wireless communication systems for improving the signal to noise ratio and for interference rejection. By multiplying the transmitted signal with a beamforming weight vector, an increased directionality is achieved for the particular signal by a transmission in a narrow beam.

Many communication systems utilize a dedicated traffic signal for transmission of each of the user's data and a common pilot signal for estimation of the channel between the transmitter and receiver. The pilot is a known signal utilized by all users connected to the base station. Hence, it is necessary to transmit the pilot over the whole coverage area of the base station. If the traffic signal to a particular user is transmitted using a different radiation pattern than the pilot, there will be a phase mismatch problem in the receiver due to the scattering in the channel.

This phase mismatch implies that there will be a rotation of the transmitted modulation constellation, which induces an increased bit error probability and thereby reduces the capacity of the system. The phase mismatch will have even more serious consequences in higher order modulation schemes such as QPSK and M-QAM.

There is a clear need for minimizing this phase mismatch in the receiver. The situation is complicated by the fact that the phase mismatch is channel dependent and the downlink channel is unknown at the transmitter. This is due to that different frequencies are used in uplink (user to base station) and downlink (base station to user) in frequency division duplex (FDD) systems and this makes the uplink and downlink channels different. However, some properties such as the direction of arrival of the impinging signal of the uplink channel and the corresponding downlink channel is the same. Hence there is some structure in the uplink and downlink channel coefficient matrices that can be utilized to reduce the phase mismatch in the receiver.

Patent of which publish number is WO 02/073826 i.e. reference 1 discloses system and method for providing phase matching with optimized beam widths, where the uplink pilot signal from the user is beamformed using two different weight vectors and a product metric between the two weighted signals is calculated. The first signal is the received pilot beamformed with the downlink pilot weight vector and the second is the same received pilot signal beamformed using one out of a set of B pre¬ defined downlink weight vectors. This is made for all B weight vectors and the B product metrics are independently filtered with smoothing filters and a decision is made which one of the B pre-defined weight vectors that are mostly suitable for the downlink transmission.

In the above patent, although there are one out of a set of B pre-defined downlink weight vectors used for beamforming downlink dedicated traffic signals, the weight vectors are pre-defined without being taken account of downlink variety and it is possible that the used weight vector is not optimal for the downlink transmission, which will induce phase mismatch.

Summary of the Invention

The object of the invention is to provide a method for calculating a downlink beamforming weight vector so that an optimal weight vector can be obtained and used for the downlink transmission.

The object is achieved with the following scheme:

A method for calculating a downlink beamforming weight vector in a wireless communication system where a pilot channel and a traffic channel beamforming weight vectors are independently chosen, comprising, a) estimating an uplink channel to obtain its coefficient matrix; b) calculating a gram matrix of the uplink channel coefficient matrix; c) filtering the gram matrix; d) finding the downlink beamforming weight vector by maximizing a product of the downlink beamforming weight Hermitian transpose and the filtered gram matrix and the pilot weight vector.

The method further comprises, e) compensating the downlink beamforming weight vector for the difference in uplink and downlink frequencies.

Between step c and step d, the method further comprises, compensating the filtered gram matrix in the /th time slot for the difference in uplink and downlink frequencies.

Comparing to the reference 1, the present invention has the advantages as following.

1. It finds the optimal weight vector for the downlink transmission directly using an analytical expression, instead of searching for the best weight vector among a set of B weight vectors. In this way, the bit error rate is lower than that of the prior art.

2. It utilizes the estimated channel coefficient matrix obtained from the uplink channel estimation so that a new analytical expression can be used to find the optimal weight vector.

3. The gram matrix of the channel coefficient matrix is filtered in the smoothing filter instead of the B outputs of the product metrics.

4. Compensation is made for the difference in uplink and downlink frequencies, which services to optimize the downlink beamforming weight.

Brief Description of the Drawings

Figure 1 shows the flowchart over the present invention for downlink beamforming;

Figure 2 shows simulation result of BER as a function of Eb/NO at an angular spread of 11°;

Figure 3 shows simulation result of bit error rate as a function of angular spread at a fixed Eb/N0=2 dB in Rayleigh fading channel with four resolved multipaths;

Figure 4 shows simulation result of required Eb/NO to maintain BER=0.001 as a function of angular spread. Embodiments of the Invention

The present invention relates to a downlink beamforming approach for code division multiple access system (CDMA) where the channel estimation in the receiver is made using a pilot signal that covers a larger portion of the cell than the traffic signal. The proposed invention uses a filtered version of the uplink space-time covariance matrix and a novel analytical formula to determine the optimal downlink transmission weight vector. The present invention shows significant improvement over a previous patent application.

Principles on the invention will be illustrated as following, If a code division multiple access (CDMA) system employing a Rake receiver is used, the receiver can collect energy from a number of multipath components of the transmitted signal. After the Rake combiner in the receiver, the decision variable for symbol n is,

U (n) = w_d ^* _ataH_DLH_DL ^*w_pilotx(ή) + Interference and noise (1)

where w_data is the weight vector for the traffic signal, w _ilot is the weight vector for the pilot signal, x(ri) is the transmitted symbol and ^* denotes Hermitian transpose. Furthermore, H_DL is an NxL downlink channel coefficient matrix where N is the number of antennas and L is the number of resolved multipaths in the receiver. If BPSK modulation is used, the detection consists of taking the real part of the expression (1), and if high order modulation formats are used such as QPSK, M- QAM,..., the detection function is more complicated but is still operating on the decision variable (1).

In view of the expression (I)₅ the desired part of T=w_dalaH_DLH_DL ^*w_pilol by

choosing w_data is optimized so that the complex scalar Y =w_data H_DLH_DL w_pilot has as small argument as possible and as large amplitude as possible relating to the term of Interference and noise. This services to improve the signal to noise ratio and for interference rejection. Ideally, T should be a positive, real scalar with as large amplitude as possible. If the downlink channel is known at the transmitter, the optimizing transmit weight vector can simply be calculated as ϊ?_rfαto = H_DLH_DL w _llot , and then normalized if desired. The transmit weight vector w _Uot used for the pilot in the expression (1) is known and fixed, but the downlink channel matrices H_DL are in FDD systems unfortunately unknown at the transmitter because downlink channel is different from uplink channel. However, it is well known that albeit H_DL is unknown, some long-term behavior properties of the product H_DLH_D ^* _L and the corresponding uplink matrix product H_ULH_U ^* _L show similarities that can be utilized. This is also cited in the reference 2.

Based on the above analyses, referencing the figure 1, the method for calculating an optimal downlink weights comprises:

Step 10, in the fth time slot, estimating the uplink channel H_UL; Step 11 , forming the gram matrix R^w according to R^(l) = H_υLH_υ ^* _ι

Step 12, filtering the gram matrix R^w with a smoothing α-filter as R_α^αR^+Cl-o^R_a^where α is a design parameter and has a value between 0 and 1 ;

Generally α can be chosen according to the channel environment where the wireless communication system is situated. If it is chosen close to 1, the smoothing filter forgets the history of the spatial covariance matrix fast and the output relies to a great extent on the most recent estimate of the channel matrix. This is useful if the channel environment changes very rapidly. If it is chosen close to 0, the smoothing filter has a long memory and the output consists of an average of spatial covariance matrices estimated over a long time history.

Step 13, compensating the filtered matrix R_« ^(l) for the difference in uplink and downlink frequencies in case of FDD system; in case of TDD system, compensation can be omitted. Wherein the compensated matrix R_α ^w is denoted as R_α ^ω'.

The compensation method can be referenced to reference 7, which comprises, averaging the filtered matrix R_α ^w; estimating an azimuthal power spectrum (APS) from the averaged matrix R_α^ ; modifying the APS; constructing the matrix R_β^\

Step 14, finding the transmit weight vector w_data by maximizing

, which is achieved by choosing w_data = R^'w^ . The method can be applied to beamforming in FDD systems such as W-CDMA and IS-95 CDMA systems where the receiver estimates the channel using a pilot signal that is common to all users and thus transmitted over the whole sector. Of course, the method is also applicable to systems where the uplink and downlink channels are equal, such as TDD systems. In this case no filtering is necessary and α=l.

In the above steps, the compensation of the different uplink and downlink frequencies can in an alternative method be done directly on the transmit weight vector instead of on the filtered matrix R_α ^(l) . In other words, after step 12, the transmit weight vector w_data is found according to step 14, and then compensate the resulting weight vector w_data for the difference in uplink and downlink frequencies in case of FDD system; in case of TDD system, compensation can be omitted. Namely, transform the resulting weight vector from uplink to downlink frequency. Manner of compensating the resulting weight vector works well only in a low angular spread environment.

The filtering of the matrix R₀^ can take any form and need not have the structure of the proposed α-filter. For instance, other methods to estimate downlink matrices from uplink received data can be utilized. An example is given in reference 6.

Although the embodiment uses the beamforming pilot signal, the present invention can be used in the case when the pilot is transmitted from a single antenna. This is obtained by letting the pilot weight vector consist of a single "1" for the particular antenna and the rest of the weight vector elements are all zeros.

Derivation of the expression (1) is illustrated as following. A direct sequence code division multiple access (DS-CDMA) system is assumed here but the derivation is general for any CDMA systems where each user is allocated a distinct pseudo-noise (PN) code and a Rake receiver is used.

Assume a direct sequence-code division multiple access (DS-CDMA) system where the base station has N transmitting antennas in a uniform linear array and assume that a receiver with a single antenna for reception is connected to the base station. The received burst can be written in baseband as N K L M₁-X , ^r(0 = ∑∑∑ ∑ < Λ_kh_nJx_k(m)s_m ^k {t -mT_s ^k -T₁) n=l Ic=I I=I m=0 ,~s

where K is the number of active users, L is the number of paths in the channel and

•

< is the complex weight for user k and antenna n

• is the complex weight for the pilot channel at antenna n

• A is the amplitude of the signal to user k

• is the amplitude of the pilot channel

• Ki is the complex channel from antenna n and path /

• ^τι is the delay for path /, assumed to be same for all antennas

• x_k O) is the symbols sent to user k in the burst, m-0, ...,M_k-I

• ^bp,lot (^m) is the pilot symbols in the burst, m=0, ...,Q_P-1

• τ^k.τ. is the period of data symbols and pilot symbols respectively

• M_k is the is the number of symbols in the data burst for user k

• Q_p is the number of pilot symbols

The weights in (2) are conjugated to make the notation correct later on. The user k (respectively, the pilot) specific spreading waveform is denoted by s_m ^k (t)

(respectively s_m (t) for the pilot), which

4 (0 = (3)

where R_k is the user specific spreading factor. The normalization in (3) implies that J^"! j* (f) I² dt = 1 and £j s_m (t) \² dt = 1 . Furthermore, ωf (i) is the i?_rchip

channelization code and C_scr(i) is a scrambling code. The two codes are mixed in a single time varying and user k specific spreading code c_k (i, m) . The pulse shaping filter is p(t) and T₀ is the chip duration. Finally, v(t) in (2) is an AWGN term with two-sided power spectral density No/2.

Now, assume that user k' is of interest, the received signal in the receiver passes through a bank of filters matched to the delayed version of s_m ^k (t) and sampled at time instants ηT_s ^{k '} +^•£,. , for each path /' where τ_v is the estimated path delay of path /'. Hence, the output of the matched filter, matched to path /' is

and if define

C_k ^k,i(η,m) = fjf (t-ηT^k' -τ_r)s_m ^k (t-mT^k -τ,)dt

C_k ^ι _Ψ(η,m) =

-τ_r)s_m (t-mT_p -T₁)Ut

expression (4) is expanded as

(5)

The "useful" term in (5) is

∑h_n/wfA_k,x_k,(η)C£f (η,η) (6)

«=i

All other terms are interference terms due to inter-path interference from both other user and own traffic channel and the common channels. Introduce the equivalent downlink channel for user k by defining

Hence, this is the channel that the receiver "experiences" due to the beamforming. Similarly, the equivalent pilot channel is

In order to implement the maximum ratio combiner (MRC) in the k' th user's σ^k' receiver, it is necessary to estimate the channel tap weights °^r . Assume for a moment that they have been estimated. If the L paths are combined in the MRC device, the following decision variable for user Jd is obtained. Sometimes, less than all L paths are combined in the MRC device.

Now, take a look at the channel estimation in the receiver. Assume that the receiver estimates the channel coefficient gf! by averaging a number of successive matched filter outputs associated with this path. Hence, define r? = fj(t)s;(t-ηT_p - τ_r)dt (10) and as before, the inter-path interference (IPI) related term is needed. C_r'(η,m)

-τ_r)s_m (t-mT_p ^k -τ,)dt so the matched filter output (10) is written as r* = gf^o'A_pb_p (η)C[, (η, η) + Interference terms (11)

Normalize the spreading signals to have

the estimate is

The channel estimate (12) can now be used in (9) to find a closed form analytical expression for the decision variable with non-ideal channel estimation in the receiver.

If we combine (12) and (9), get

which can compactly be written as

^Uk'_Bpsκ = ™d^*ata^HH*Wpiiot A'^x _k' fø) interference Jerms (14) where the corresponding weights has been collected into a vector w = [w, W₂ ^{■ ■ ■} w_N] (15) and w_data is the weight vector for the traffic channel. The channel coefficients has been collected into the NxL matrix

where each column is the array response for a resolved multipath and each row is the channel impulse response from a single transmit antenna to the receiver antenna.

In order to prove the advantages in the invention and compare with the said patent with publish number WO 02/073826, simulation is made with a certain simulation parameters. The bit error rate (BER) for the present invention and the method of the patent with publish number WO 02/073826 are estimated assuming a BPSK modulation scheme. Channel model for simulation is illustrated as following. A model is needed for the uplink/downlink channels, here denoted H_UL and H_DL , that incorporates the correlation between the matrix elements due to limited angular spread. Therefore, assume a channel model with Q clusters of scatterers. Define a cluster as a group of L₅ scatterers with an average angle of arrival/departure angle, O₁, as seen from broadside of the array antenna. The cluster has certain dispersion in both angle and time. The angle dispersion is measured as the standard deviation of the angular spread (σ_As) and the time dispersion in the time spread (TS). Assume in the following that the TS for each cluster is less than a chip time interval, thereby each cluster corresponds to one of the L paths in the received multipath profile, which implies that in this model L=Q. thus the uplink and downlink channel models for path / can be written as reference 2 and 3

h ^UL(I) = ∑r%aφ, + θ%) (17) and h^DL(l) = ∑ηfάφ_{ι +} θ%) (18) which is described in respectively, where the array response vector is defined as (where a half-a- wavelength spaced uniform linear array with omni-directional antenna elements is assumed) α(0) = [l e^{Jπsin(θ) ■ ■ ■} e^MN-^ι)MΘ)] 14N and

axe the angles to the scatterers. Note that the uplink and downlink channel models have the same average angle of arrival θ, for the same corresponding multipath component /.

This is a key property that allows the invention to use information from the uplink beamforming in the calculation of the downlink beamforming weights. The angular spread Q_AS in the uplink and downlink channels are equal.

In the statistical channel model used in this report, assume that the scattering angles #/f ,#/f are independent and Laplace distributed referring to reference 4 and 5, that is, the probability density function, conditioned on the average angle 6>_/ is

and the complex scattering coefficients r/./V/,/'¹ are modelled as independent, zero mean, complex Gaussian random variables with unit variance. This model is justified by measurements presented in reference 3 and 4.

The channels are generated as follows.

1. Set the slot index i=l.

2. For each of the L clusters, generate the angle positions θj% of the Ls uplink scatterers from the Laplace distribution and the Ls scattering coefficients r^¹ from the complex Gaussian distribution.

3. Calculate the uplink channel matrix H_UL from the expression (17).

4. For each of the L clusters, generate new angle positions θ^ of the Ls downlink scatterers from the Laplace distribution and the Ls scattering coefficients rι_tk^DL from the complex Gaussian distribution.

5. Calculate the downlink channel matrix H_DL from the expression (18).

The SNR in the receiver after the maximum ratio combiner can be written as

O Λ/P ,_ —h L fc V d ^aa^at^ma" D ^υL^L'^ D ^UL^{L W} p Pi"lo∞t ! /Λ Tp (I Q')

^p*ilot^HDL^R _Vv^HDL W pilot where SR(») is the real part of its argument, E_b is the energy per bit and R_vv is the noise covariance matrix in the receiver. This is actually the SNR before the detector, where the received complex baseband symbol has been projected on to the real axis, since BPSK modulation is assumed.

The BER can then be calculated as the average over the channel distribution

where for each channel realization H, a weight vector for the data w_data is calculated according to a pre-defined scheme, p(H) is the probability density function of the channel matrix H.

The integral in the expression (20) is solved by a Monte Carlo method so new channels H_υLH_DL are generated and P_b are calculated until it has converged to a stable value.

The parameters used in the simulations are given in the table below.

Table 1 Parameters used in the simulation

To compare the present invention with patent with publish number WO 02/073826, a simulation was performed where uncorrelated uplink and downlink channels were generated but with equal long-term properties such as the angular spread and the direction of arrival for the multipaths. The channel had four multipaths from 14°, 16°, 18° and 20° seen from broadside and a set of B=90 beams were used in the method of the reference 1. The results are shown in figure 2, figure 3 and figure 4. Observe that the present invention outperforms the method in the reference 1, and the difference seem to increase at an increasing angular spread and/or increasing Eb/N0.

REFERENCES

[1] P.B. Wong, A.Tesler and S.B. Scherzer, "System and method for providing phase matching with optimized beam widths". Patent WO 02/073826, 19 September

2002. [2] P.Zetterberg, "Mobile Cellular Communications with Base Station Antenna

Arrays: Spectrum Efficiency, Algorithms and Propagation Models", PhD Thesis,

Royal institute of technology, Stockholm, Sweden, 1997. [3] Q.H.Spencer, B.D.Jeffs, M.A. Jensen and A.L. Swindlehurst, "Modelling the

Statistical Time and Angle of Arrival Characteristics of an Indoor Multipath [4] K.I.Pedersen, P. E. Mogensen and B.H.Fleury, "A stochastic model of the temporal and azimuthal dispersion seen at the base station in outdoor propagation environments", IEEE Transactions on vehicular technology, Vol.49, no.2 March 2000, p.437- 447.

[5] K.I. Pedersen and P.E. Mogensen, "Power azimuth spectrum in outdoor environments", IEE Electronic Letters, vol.33, no.18, pp.1583-1584, Aug. 1997.

[6] Y-C. Liang and F.P.S. Chin, "Downlink Channel Covariance Matrix (DCCM) Estimation and Its Applications in Wireless DS-CDMA Systems", IEEE Journal on Selected Areas in Communications, vol.19, no.2, February 2001, p.222-232.

[7] Klaus Hugl, Juha Laurila and Ernst Bonek, "DOWNLINK BEAMFORMING FOR FREQUENCY DIVISION DUPLEX SYSTEMS", IEEE Global Telecommunications Conference, (GLOBECOM'99), December, 5-9, 1999, Rio de Janeiro, Brazil, p.2097-2101.

Claims

1. A method for calculating a downlink beamforming weight vector in a wireless communication system where a pilot channel and a traffic channel beamforming weight vectors are independently chosen, comprising, a) estimating an uplink channel to obtain its coefficient matrix; b) calculating a gram matrix of the uplink channel coefficient matrix; c) filtering the gram matrix; d) finding the downlink beamforming weight vector by maximizing a product of the downlink beamforming weight Hermitian transpose and the filtered gram matrix and the pilot weight vector.

2. The method according to claim 1, wherein step a further comprises, in the fth time slot estimating the uplink channel, step c comprises, filtering the gram matrix with a smoothing α-filter as R_a =αR⁽-¹-^>+(l-α)R_α , where a is a design parameter, R^ is the gram matrix in the zth time slot, R₀^ is the filtered gram matrix in the zth time slot, R_αf^1"1^ is the filtered gram matrix in the (M)th time slot.

3. The method according to claim 1, wherein step d is achieved by calculating a product of the filtered gram matrix and the pilot weight vector.

4. The method according to claim 2, wherein step d is achieved by calculating a product of the filtered gram matrix in the /th time slot and the pilot weight vector.

5. The method according to claim 1, 2, 3 or 4, wherein step b comprises, calculating a gram matrix of the uplink channel coefficient matrix according to a expression: R= H_ULH_U ^* _L , where R is the gram matrix, HU_L is the uplink channel coefficient matrix, H^₁ is Hermitian transpose of the uplink channel coefficient matrix.

6. The method according to claim 1, 2, 3 or 4, after step d the method further comprises, e) compensating the downlink beamforming weight vector for the difference in uplink and downlink frequencies.

7. The method according to claim 2 or 4, between step c and step d, the method further comprises, compensating the filtered gram matrix in the fth time slot for the difference in uplink and downlink frequencies; step d further comprises, finding the downlink beamforming weight vector by maximizing a product of the downlink beamforming weight Hermitian transpose and the compensated filtered gram matrix and the pilot weight vector.

8. The method according to claim 2, wherein α is 1 in case of a TDD system.

9. The method according to claim 1, wherein the pilot weight vector consists of a single "1" for a single antenna used for transmitting a pilot, and the rest of the pilot weight vector elements are all zeros.